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Manuscript Title: Inversion of Abel's integral equation - application to plasma spectroscopy.
Authors: C. Fleurier, J. Chapelle
Program title: ABEL
Catalogue identifier: AAAC_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 7(1974)200
Programming language: Fortran.
Computer: IBM 360/25.
Operating system: DOS/360.
RAM: 7K words
Word size: 32
Keywords: Plasma physics, Spectroscopy, Abel integral equation, Least squares, Approximation, Data interpretation.
Classification: 19.4.

Nature of problem:
The purpose of this program is to determine the radial distribution of the emission coefficient from the measured intensity distribution emitted by an extended source of radiation, particularly a plasma source. The source is assumed to be optically thin and axially symmetrical.

Solution method:
This problem is solved by inverting Abel's integral equation. A smoothing procedure is made on the experimental curve in order to attenuate the random errors before computing the derivative. The integral is calculated analytically in a small interval on the right of the discontinity point, the other part is estimated numerically.

The computation is nearly entirely numerical and needs equally spaced points for the data.

Running time:
For an experimental curve defined by 21 points the calculation time is less than 30 s on the IBM 360/25 computer.